What is unequivocally proven, however, is that violent crime rates (with murder included) go up dramatically when you take guns away.

Unequivocally? To prove something unequivocally you would need to find two environments where everything is the same. Everything. Except guns. That is clearly not possible so at best you could suggest violent crime may go up when guns are taken away.
And that is a hypothesis I would disagree with.

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We compare to the UK, Canada and Australia because we have somewhat similar societies, where the amount of gun control is the only real variable.

What?! You serious?
Guns the only real variable?!

Alabama Shooter had it right with:

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This whole concept of comparing everything we do to the UK, Australia or Canada really needs to stop.

As did Jimbob with:

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Why the continued fixation on "gun deaths"?

The interested parties of the US (for or against guns) need to really stop a) looking for simplistic single reasons for the incidence of gun violence and b) looking beyond its borders for those reasons, justifications and validations....

If the problem exists in the US, then you can be sure the reasons for and solutions to this will have originated in US society and will be the result of a myriad of factors that have been developing and evolving over decades.

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You cannot wake someone who is pretending to sleep. Stop pretending. Wake up.

Freedom: Please enjoy responsibly.

Any idea that relies on murder for its survival in intrinsically weak.